The human brain constitutes an impressive network formed by the structural and functional connectivity patterns between billions of neurons. Modern functional and diffusion magnetic resonance imaging (fMRI and dMRI) providesunprecedented opportunities for exploring the functional and structural organization of the brain in continuously increasing resolution. From these images, networks of structural and functional connectivity can be constructed. Bayesian stochastic block modelling provides a prominent data-driven approach for uncovering the latent organization, by clustering the networks into groups of nodes with a shared connectivity pattern. Modelling the brain in great detail on a whole-brain scale is essential to fully understand the underlying organization of the brain and reveal the relations between structure and function, that allows sophisticated cognitive behaviour to emerge from ensembles of neurons. Relying on Markov Chain Monte Carlo (MCMC) simulations as the workhorse in Bayesian inference however poses significant computational challenges, especially when modelling networks at the scale and complexity supported by high-resolution whole-brain MRI. In this thesis, we present how to overcome these computational limitations and apply Bayesian stochastic block models for un-supervised data-driven clustering of whole-brain connectivity in full image resolution. We implement high-performance software that allows us to efficiently apply stochastic blockmodelling with MCMC sampling on large complex networks. To obtain the necessary computational performance, we find that both hardware and model specific properties must be taken into consideration - to an extend not supported by generic modelling tools. Computational overhead is reduced by an approach, where key values are cached to avoid re-computations, while tablelookups are utilized for frequently computed special functions. The efficient memory-management of C++ is utilized to implement dedicated data-structures, optimized to facilitate performance-critical operations related to the inference procedure. Furthermore, the software is based on a modular design, which allows us to couple and explore different models and sampling procedures in runtime, still being applied to full-sized data. Using the implemented tools, we demonstrate that the models successfully can be applied for clustering whole-brain connectivity networks. Without being informed of spatial information, the data-driven models can discover spatial homogeneous regions that are meaningful and in agreement with existing anatomical atlases. We further demonstrate that structural and functional connectivity share information, allowing us to jointly model both modalities. For limited, noisy fMRI data we find that integrating structural information aids in discovering the functional organization better than using the fMRI data alone. Though structure and function describes very different properties of the brain, we find that probabilistic modelling provides an intuitive data-driven approach for uncovering the latent organization in connectivity networks. We find that the stochastic block models can be computationally scaled to model wholebrain connectivity, and by doing so allows us to better utilize the full potential of high-resolution MRI and advances our understanding of both the functional and structural organization of the entire brain.